Making a Mathematical Statistics Course More Modern

USCOTS 2025

Jessica Chapman

St. Lawrence University (USA)

Matt Higham

St. Lawrence University (USA)

2025-07-18

Who Are We

slide about Jessica

Who Are We

slide about Matt

Your Turn

Form groups of 3 to 5 people with those around you. Introduce yourselves and INSERT SOME INTRO QUESTION.

04:00

Motivation

  1. What more can we do to make math stat more “useful?”
  2. ADD OTHER GOALS HERE AFTER MORE IS FLESHED OUT

What Do We Mean by “Math-Stat”?

Motivation: Student Feedback

Feedback A

“I really only think this class is applicable to someone going to grad school or heavily love mathematics. The class is great in that it is difficult and extends your math but very low applicability to life/career.”

Feedback B

“There are so many components of this course that I will be able to apply to my future career and life experiences, a lot of which I think everyone regardless of field of study should at least know a little about.”

Activity

What does it mean for a math-stat course to be “useful?” In your groups, try to come up with a specific definition for “useful” in this context.

04:00

What Our Students Said (Top 3 Response Types)

  • Applicable to Future: “I defined useful as something I think I will continue to use or see again in the future—skills or ideas that expand into future learning goals.”
  • Applicable to the “Real World”: “I based this on how applicable these things would be to my professional life or general knowledge after college….”
  • Deepened Understanding: “I (also) considered how much something deepened my conceptual understanding.”

Is Math Stat “Useful?”

  • Could math stat be more “useful?”

  • JSM 2003 Session “Is the Math Stat Course obsolete?”

Activity: In or Out?

Activity: Short Story

  • Fostering Conceptual Understanding in Mathematical Statistics by Green and Blankenship (2015).
    • published in The American Statistician.

Activity: Short Story

A “meaningful story” is one continuous piece of writing / creative work that uses key words from a list and in which the sentences “make sense and hang together.” That is, the ideas in the story must illustrate that you understand key concepts from math-stat in a way that allows you to write “meaningfully” about them. It is your job to use the terms in a way that demonstrates that you understand the statistical concepts involved and why we care about these terms in the big picture of statistical theory.

Activity: Short Story

With your small group, orally contruct a meaningful paragraph about a topic that you will draw from a hat using 3 of the following 5 terms:

  • Estimator
  • Estimate (as a noun)
  • Parameter
  • Bias
  • Variance
05:00

What Our Students Wrote About

  • 80’s music.
  • applying to jobs (this is a spring semester course of mostly seniors!).
  • gender inequality in women’s and men’s hockey.
  • living on a farm.
  • all kinds of sports!

What a Student Said

“The second mini-project was the most impactful assessment for me….This project was very different from much of the Math/Stat curriculum and a unique opportunity to show understanding of different terms. Being forced to use these terms in the context of a sentence helps to develop a better understanding of what they mean. It is difficult to explain terms like estimator, variance, or binomial distribution in a statistical context of a story without a good understanding of their meanings….”

Activity: Bayes

Activity: p-value Paper

Wasserstein, R. L., Schirm, A. L., & Lazar, N. A. (2019). Moving to a world beyond “p< 0.05”. The American Statistician, 73(sup1), 1-19.

“Moving beyond ‘statistical significance’ opens researchers to the real significance of statistics, which is ‘the science of learning from data, and of measuring, controlling, and communicating uncertainty’ (Davidian and Louis 2012).”

“These p-values We’ve Been Using for 4 Years Are Flawed??”

Activity: p-value Paper

On Handout.

07:00

What Our Students Said

“I always considered p-values to be the best way to measure significance and did not question what a p-value really meant. The project taught me what statistical thinking is and to take into account more than just whether a p-value passes some threshold. In intro statistics, we are taught to follow specific steps and formulas without much background knowledge or reasoning. I am someone who does not often question information, especially in classes…..”

What Our Students Said

“(The p-value paper) was probably the most thought-provoking assignment for me because it forced me to think critically about how we conduct research. Coming from an Economics background, there is a lot of conversation around the reliability or quality of research. I felt that this assessment was the most impactful for me long-term because it forced me to think critically about something that I had previously just taken for granted….”

Activity: Assessment

Modernizing Undergraduate Stat. Theory Course